Average Error: 0.1 → 0.0
Time: 6.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r353599 = 1.0;
        double r353600 = 4.0;
        double r353601 = x;
        double r353602 = y;
        double r353603 = 0.75;
        double r353604 = r353602 * r353603;
        double r353605 = r353601 + r353604;
        double r353606 = z;
        double r353607 = r353605 - r353606;
        double r353608 = r353600 * r353607;
        double r353609 = r353608 / r353602;
        double r353610 = r353599 + r353609;
        return r353610;
}
↓
double f(double x, double y, double z) {
        double r353611 = 4.0;
        double r353612 = x;
        double r353613 = z;
        double r353614 = r353612 - r353613;
        double r353615 = y;
        double r353616 = r353614 / r353615;
        double r353617 = r353616 * r353611;
        double r353618 = r353611 + r353617;
        return r353618;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(0.75 + \frac{x - z}{y}\right) + 1}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 4\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4 + \frac{x - z}{y} \cdot 4}\]

  5. Final simplification0.0

    \[\leadsto 4 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))